Abstract
For a simple graph G = (V, E), a vertex labeling phi : V -> {1, 2, ... k} is called k-labeling. The weight of an edge xy in G, denoted by w(phi)(xy), is the sum of the labels of end vertices x and y, i.e w(phi)(xy) = phi(x) + phi(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f , there is w(phi)(e) not equal w(phi)(f). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G).
In this paper, we determine the exact value of edge irregularity strength for categorical product of two paths.